The present invention relates generally to methods for audio signal bandwidth compression and to digital audio test and measurement systems. In a specific application, the present invention applies to the generation of sinusoidal test signals in MDCT-based (modified discrete cosine transform) coding formats for testing the audio performance of devices which accept and decode such signals.
MDCT-based audio codecs are in widespread use today for the purposes of reducing transmission bandwidth or storage requirements for digital audio programs. Using the MDCT, it is possible to obtain a critically sampled (i.e. no redundant information) transform representation with 50% overlapping signal blocks. When analysis/synthesis windows satisfying the symmetry requirements of TDAC (time domain aliasing cancellation) are used, the MDCT is perfectly invertible. For more details refer to Princen and Bradley, “Analysis/Synthesis Filter Bank Design Based on Time Domain Aliasing Cancellation,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-34, No. 5, October 1986, pp. 1153-1161.
Audio codecs using the MDCT include Dolby® AC-3, MPEG-1 Audio Layer 3, and MPEG-4 AAC. Generally speaking these codecs use the MDCT as a time to frequency transformation and transmit quantized MDCT coefficients at a reduced bitrate for synthesis in the decoder. Psychoacoustic models are employed to determine the perceptual relevance of the various spectral components which result from each block MDCT. Based on these models, MDCT bins containing little energy or those which are perceptually masked by nearby dominant frequencies are quantized with fewer bits of resolution.
Many devices for home audio, mobile audio, wireless communications, etc. now accept coded audio as a primary input audio format. For testing such devices it is convenient to deliver MDCT-coded test signals directly to the audio decoder in the device under test (DUT). There are many classes of signals which are used as stimulus for audio testing applications but by far the most commonly employed is the sinusoid. Sinusoidal signals are nearly ubiquitous for testing applications since they are eigenfunctions of any linear time invariant (LTI) system. Frequency and phase response may be computed by observation of the amplitude and phase relationship of input and output sinusoids at the frequencies of interest. In addition, sinusoidal test signals may be useful for characterizing the non-linear behavior of a system. Distortion products can appear in many forms, but are most easily identified by spurious (i.e. unwanted) spectral components appearing at the device output in response to a stimulus of one or more sinusoidal test signals.
U.S. Pat. No. 5,357,594 (Fielder) discloses a system for subband audio coding employing a specially designed analysis-synthesis window. The Kaiser-Bessel Derived (KBD) window is constructed by a normalization process applied to an ordinary Kaiser-Bessel window such that the resulting window satisfies the TDAC perfect reconstruction conditions. The KBD window allows a convenient parametric tradeoff between main lobe width and side lobe attenuation by adjustment of the window parameter α. The Dolby® AC-3 codec uses the KBD window (α=4) as a symmetric analysis-synthesis window for the MDCT.
FIG. 1 generally depicts a prior art system for delivering sinusoidal test signals using a conventional prior art coding system similar to that disclosed in Fielder's patent. First is an apparatus for generation of a sinusoidal sequence 110, which may be implemented by a number of known methods including wave tables, Taylor series approximation or with a digitally implemented oscillator. This sequence is provided as input to a conventional MDCT-based audio codec 120, contained in FIG. 1 by a dashed line boundary. The input sequence is conventionally divided into 50% overlapping blocks and windowed 121 with an appropriate window sequence satisfying TDAC symmetry requirements. Windowed signal blocks are sent to an MDCT transformer 122 which produces a set of real-valued transform coefficients. The resulting MDCT coefficients are provided as input to a subband bit allocation process 123, which will typically employ a psychoacoustic masking model to minimize the perceptual impact of subband quantization with a given bit allocation budget. Based on the bit allocation thus produced, the MDCT coefficients are quantized 124 and assembled 125 into a properly formatted bitstream. This bitstream leaves the codec 120 and is finally transmitted or stored 130 for later decoding.
There are firms presently offering coded test signal generation systems which follow the lines of the exemplary prior art system 100. Audio Precision offers the OPT-2711 Dolby® Digital Generator upgrade to their 2700 series audio analyzers. The combined system contains a test signal generator followed by an encoder and hardware for delivering test signals in an AC-3 bitstream transmitted on an IEC-61937 interface. The OPT-2711 and similar devices employing this paradigm for the generation of MDCT-coded sinusoidal signals have the computational tasks of independently generating low-distortion sinusoidal sequences, windowing and performing the MDCT on this data, as well as computing bit allocations, quantizing and properly formatting the resultant bitstream.
A commonly encountered definition of the MDCT is:
      X    ⁡          [      k      ]        ≡            ∑              n        =        0                    N        -        1              ⁢                  w        ⁡                  [          n          ]                    ⁢              x        ⁡                  [          n          ]                    ⁢                        cos          ⁡                      [                                                            2                  ⁢                                                                          ⁢                  π                                N                            ⁢                              (                                  n                  +                                      1                    2                                    +                                      N                    4                                                  )                            ⁢                              (                                  k                  +                                      1                    2                                                  )                                      ]                          .            
Evaluated directly the MDCT requires O(N2) computations per block. Fortunately more efficient methods of computing the MDCT have been devised in recent years. U.S. Pat. No. 6,430,529 (Huang) and U.S. Pat. No. 5,592,584 (Ferreira and Johnston) describe techniques for MDCT computation having an asymptotic complexity of only O(N log2N). These faster methods exploit the fact that the MDCT is mathematically equivalent to a time and frequency-shifted DFT. Using this equivalence the MDCT may be computed as a composition of FFT and complex pre- and post-multiplications.
It is desirable for many applications to further reduce the computational and memory requirements of producing MDCT-coded sinusoidal test signals. Unfortunately the MDCT has relatively complex mathematical properties when compared with other common discrete transforms. Many useful and important theorems which apply to a time-invariant transform such as the DFT do not apply directly to the MDCT. Most significantly to this disclosure, it is not possible to produce the MDCT of a time-translated sinusoid by simple multiplication with a phasor sequence in the transform domain.
An analytical approximation to the MDCT of a sinusoid is due to L. Daudet and M. Sandler, in “MDCT Analysis of Sinusoids: Exact Results and Applications for Coding Artifacts Reduction,” IEEE Transactions on Speech and Audio Processing, Vol. 12, No. 3, May 2004, pp. 302-312. The authors assumed that a basic sine analysis window was used, and with a few other simplifying assumptions, the authors derived an approximation to the MDCT of a sinusoid for the purpose of understanding some common audible artifacts in MDCT-based audio codecs. However the authors did not present results which may be extended easily to other analysis/synthesis windows, and the approximation presented is unsuitable for low-distortion waveform synthesis. Moreover, the results derived in their paper became very poor at the extremes of the spectrum (i.e. for sinusoids with discrete-time frequency Ω close to extremal values 0 or π).
U.S. Pat. No. 7,058,571 (Tshushima, et al) discloses a method for injecting sinusoids into a single band of a real-valued filter bank (e.g. MDCT) while suppressing aliasing products that can appear in adjacent subbands. The method presented in Tshushima's patent is limited however to the synthesis of sinusoids at the center frequency of a filter bank subband. Furthermore the simple two-band aliasing suppression model Tshushima employed is insufficient for low distortion sinusoid synthesis with the MDCT. In the MDCT of a sinusoid there are a large number of MDCT coefficients which contribute significantly to the reconstructed waveform. The compensation signals disclosed by Tshushima therefore do not suffice for test and measurement applications where extremely low waveform distortion is required.
In light of the above and other considerations there is a need for a computationally efficient and accurate means for computing the MDCT of a sinusoidal signal. The method and/or apparatus should work well at any desired sinusoid frequency including extremes of the discrete-time frequency spectrum and away from MDCT bin center frequencies, and should be adaptable for compatibility with any analysis-synthesis window with excellent distortion performance.